Sussex police are collaborating with French gendarmes in a cross-Channel search for a missing schoolgirl believed to have run away with one of her teachers.

Megan Stammers, 15, failed to turn up for school on Friday and is known to have crossed from Dover to Calais later that evening. Police believe she may be in France with Jeremy Forrest, 30, from Ringmer in East Sussex, who is a maths teacher at Megan's school in Eastbourne.

The Lewes district commander, Chief Inspector Jason Tingley, saidon Sunday that investigators were pursuing several lines of inquiry and were at a critical stage in their inquiries.

"I would like to appeal to anyone who knows Megan and has not spoken to us to please get in touch," he said in a statement. "Her family are incredibly worried and want her to come home. Your call will be dealt with in the utmost confidence."

The alarm was raised over Megan's disappearance just after midday on Friday, when, despite having set off from her home in Eastbourne, the teenager did not arrive at school.

Police have said she crossed over to Calais at around 9.20pm that evening.

On Saturday, her father, Martin Stammers, urged Megan to get in touch with her family. "We just want Megan to make contact with us," he said. "We are worried and miss her terribly. Please get in touch, Megan."

On Twitter, where he has been co-ordinating an online attempt to find his daughter, he added on Sunday: "Have to remain strong for Meg's, can't dwell in the misery of 'what ifs' – we love you sweetheart, doing all we can."

The teenager's cousin, Chloe Stammers, has also been spreading information of her relative's disappearance on Twitter. On Sunday morning she wrote: "Was hoping that I woke up this morning and this was all a nightmare!" Earlier she had said: "We need our Meg home!"

Officers have said they do not believe Megan to be at risk, but they have contacted the French authorities in order to try to locate her. They have circulated the registration number, GJ08 RJO, of a black Ford Fiesta they says belongs to Forrest and have been examining CCTV images to try to establish the teenager's whereabouts.

There have been no reported sightings of her since she disappeared.

In a statement, Tingley said: "We are at a critical stage of the investigation… We are investigating several lines of inquiry and are grateful for the support and cooperation from Megan's family and friends."

Megan is described as 5' 6", of slim build, with long dark brown hair. Police say she was last seen wearing a white vest top and a silver necklace.

A statement on the website of Bishop Bell, a Church of England computing and mathematics school, said: "We are extremely concerned about a missing pupil and, if anyone at all has any information, we would urge them to contact the police as a matter of urgency."